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Math Help - Integration

  1. #1
    Newbie leibnitz's Avatar
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    Integration

    Pls fans help me out with this problem........n3/square root n+1

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  2. #2
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    Re: Integration

    what's the question?
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  3. #3
    Forum Admin topsquark's Avatar
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    Re: Integration

    Quote Originally Posted by leibnitz View Post
    Pls fans help me out with this problem........n3/square root n+1
    I think you attached the wrong file?

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  4. #4
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    Re: Integration

    Assuming the OP meant to write \displaystyle \begin{align*} \int{ \frac{ n^3 }{ \sqrt{ n + 1 }}\,dn} \end{align*}, a substitution of the form \displaystyle \begin{align*} u = n + 1 \implies du = dn \end{align*} is appropriate, giving

    \displaystyle \begin{align*} \int{ \frac{n^3}{\sqrt{n+1}}\,dn} &= \int{ \frac{\left( u - 1 \right) ^3}{\sqrt{u}}\,du} \end{align*}

    Now expand the numerator, divide each term by \displaystyle \begin{align*} u^{\frac{1}{2}} \end{align*}, and integrate.
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